There are 38 cube houses. Each house could hold 1,000 unit cubes that are 1 meter by 1 meter by 1 meter. Describe the dimensions of a cube house using unit cubes. Remember that the edges of a cube are all the same length.

Answer:

315

Step-by-step explanation:

If 70 children is 2 parts, one part is 35

35*9 is 315

Answer:

315 adults

Step-by-step explanation:

2:9 where 2 is children and 9 is adults.

2 = 70, therefore 1 = 35

35 x 9 = 315

To find the one-sided limit of the function f(x) = (x-9)² as x approaches 9 from the left (x → 9-), we need to evaluate the expression (-9)². The result of this calculation is 81, indicating that the one-sided limit of f(x) as x approaches 9 from the left is 81.

The expression (-9)² simplifies to 81. This means that as x approaches 9 from the left (x → 9-), the function f(x) = (x-9)² approaches the value 81. Therefore, the one-sided limit of f(x) as x approaches 9 from the left is 81.

It's important to note that this result is specific to the left-hand side limit.

To find the two-sided limit (if it exists), we would need to evaluate the limit as x approaches 9 from both the left and the right and ensure that the values match.

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The correct option is E. The population mean is less than 125. As, 125 is does not comes in the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

The 90% confidence interval for the mean of the population is computed to be 135 to 160. This means that we are 90% confident that the true population mean falls within this range.

Since 125 is not within the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

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The latest statistics from the National Science Foundation indicate a concerning Gender gap persists in computer science and engineering fields with declining women's degrees from 2005 to 2008.

The data shows that the percentage of engineering degrees awarded to women decreased from 20% in 2005 to 18% in 2008, while the percentage of computer science degrees awarded to women dropped from 22% to 17% during the same period.

These findings highlight the persistent gender disparity in these fields, despite progress in other areas. To address this issue, efforts should focus on promoting and encouraging women to pursue careers in computer science and engineering, providing equal opportunities and supportive environments to bridge the gender gap and foster diversity and inclusion in these crucial fields.

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The missing data value according to the given z-score is 39.

We can determine how distant a data point is from the mean using its z-score. It is a crucial subject in statistics. Z-scores are a way to compare data to a population that is considered "normal." When attempting to compare someone's weight to that of the "average" person, for instance, it might be intimidating to look at a large table of data even though we know they weigh 70 kg. A z-score offers us an indication of how that person's weight compares to the mean weight of the general population. We shall discover what the z score is in this post.

The z score is a measurement of how many standard deviations a raw score is below or above the population mean. If the value is higher than the mean, it will be positive; if it is lower, it will be negative. The standard score is another name for it. It shows how far away from the mean an object is, in terms of standard deviations. The mean and population standard deviation must be known to apply a z-score. The likelihood of a score happening inside a typical normal distribution may be calculated with the use of a z score. We may also compare two scores from other samples thanks to it. A z score table is a table that contains the values of, which represent the cumulative distribution function of the normal distribution.

The equation is given by z = (x – μ)/ σ.

μ = mean

σ = standard deviation

x = test value.

In the question, z = -2.1, μ = 43, and σ = 2.

Substituting the values, we get:

-2.1 = (x - 43)/2,

or, x - 43 = -2.1*2,

or, x = -4.2 + 43,

or, x = 38.8 ≈ 39.

Thus, the missing data value according to the given z-score is 39.

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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Answer:

B, 5x - 3 = 12

Step-by-step explanation:

3 less means subtracting, it's going to be -3.

It says 3 less than five times a number, meaning we don't know the number, so we can put it as x.

3 less means your subtracting from something, which would make it 5x - 3.

Finally, they state that it equals 12, making the equation 5x - 3 = 12.

Answer:

4/15~15.5

Step-by-step explanation:

In a right triangle, the sum of the squares of the

lengths of the legs is equal to the square of the length

of the hypotenuse. The length of the hypotenuse is 16

and the lengths of the legs are 4 and x.

Answer:

2.9 per second

Step-by-step explanation:

The height of the triangular base is 65 inches.

The volume of the triangular prism is 205920 inches³.

The diagram above is a triangular base prism. The volume of the prism can be found as follows.

We need to find the height of the triangular base of the prism using Pythagoras's theorem.

Hence,

c² = a² + b²

97² - 72² = h²

h² = 9409 - 5184

h = √4225

h = 65 inches

Therefore,

volume of the triangular prism = Bh

where

B = 1 / 2 × 72 × 65

B = 4680 / 2

B = 2340 inches²

Hence,

volume of the triangular prism = 2340 × 88

volume of the triangular prism = 205920 inches³

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Answer:

Step-by-step explanation:

-1

Answer:

Y = 1/3x + 4

Step-by-step explanation:

y = mx + b

m = slope and b = y-intercept

Hope this helps. Pls give brainliest.

Answer:

y=1/3x+4

Step-by-step explanation:

The slope-intercept from is y=mx+b. the given information provides with the m/slope, but we are missing the b/y-intercept. to find the value we can plug in the x and y values with the given coordinates and solve.

5=1/3(3)+b

5=1+b

4=b

now that we have a y-intercept we can write this in slope-intercept form,

y=1/3x+4

Answer:

240

Step-by-step explanation:

you have to divide 1,920 by 8

There are 1e-6 cubic meters in a cubic centimeter.

A centimeter is a metric unit of measurement used for measuring the length of an object. It is written as cm. It can also be defined as the unit of length in the International System of Units (SI), the current form of the metric system. It is equivalent to 1/100 meters.

A meter has 100 centimeters.

10 millimeters make one centimeter.

The centimeter can be written as cm.

While calculating the surface area of an object, the unit of measurement becomes cm².

While measuring the volume of an object, the unit of measurement becomes cm³.

Thus, There are 1e-6 cubic meters in a cubic centimeter.

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Answer:

V = 262.5 ft.

Step-by-step explanation:

Volume = length × width × height

6.25 × 14 × 3

6.25 × 42

262.5

Answer:

d) f(n) = 4 . 3^(n-1)

______________

The equation models mateo’s movements according to commutative property is (-15) + 4 + (-7) = 4 + (-15) + (-7). So, Option C is correct option.

According to the statement

we have given some data related the dives at the sea level. And we have to find that the which equation models mateo’s movements with the help of the commutative property.

So, For this purpose, we know that the

The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. We can define commutative property of addition as adding the numbers in any order will give the same answer. Here, a and b can be whole numbers, integers, decimals, or even fractions.

And

We are given that he dives down 15 meters, so this will be -15.

Then, he rises up 4 meters, so this is 4.

Then, he goes back down 7 meters, or -7.

So, we have (-15) + 4 + (-7).

And The commutative property states that we order the number in any way we want, and the only choice that works is (-15) + 4 + (-7) = 4 + (-15) + (-7).

So, The equation models mateo’s movements according to commutative property is (-15) + 4 + (-7) = 4 + (-15) + (-7). So, Option C is correct option.

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The two polygons are similar if the corresponding angles are congruent and the corresponding sides are proportional,the value of x is 8.

The two polygons are similar if the corresponding angles are congruent and the corresponding sides are proportional. Therefore, the ratio of the lengths of the sides of the two polygons is equal to the ratio of the measures of the corresponding angles.

In this case, the ratio of the corresponding side lengths of the two polygons is equal to the ratio of the measures of the corresponding angles. The ratio of the lengths of the two sides of the larger polygon (x-3 , 8 and 16) is (x-3)/8 : 8/16. This ratio is equal to the ratio of the measures of the corresponding angles of the two polygons, which is 2.5/2 : 2/4.

Equating these two ratios, we get (x-3)/8 = 2.5/2 and 8/16 = 2/4. Solving these two equations, we get x-3 = 5 and 8 = 4. Adding 3 to both sides, we get x = 8. Hence, the value of x is 8.Therefore, the value of x is 8.

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The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

The  given standard error of the mean for a sample of 100 is 30. So to cut the standard error of the mean to 15, we have to proceed by increasing the sample size to 400.

The  formula for evaluating the standard error of mean
SEM = SD / √(n)
here, SEM = standard error of the mean,
SD = standard deviation
n = sample size
Staging the values
15 = SD / √(100)
15 x √(100) = SD
SD = 150
Now evaluating for the value of n
15 = 150 / √(n)
15 x √(n) = 150
√(n) = 10
n = 100
Now looking at the formula, we need to decrease SEM by half,

So we proceed by increasing the  sample size by a factor of 4.

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

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By definition of the derivative,

\(\displaystyle t'(x) = \lim_{h\to0} \frac{t(x+h) - t(x)}h\)

\(\displaystyle t'(x) = \lim_{h\to0} \frac{\sqrt{-3(x+h)-7} - \sqrt{-3x-7}}h\)

Rationalize the numerator by multiplying the fraction uniformly by its conjugate:

\(\displaystyle t'(x) = \lim_{h\to0} \frac{\sqrt{-3(x+h)-7} - \sqrt{-3x-7}}h \times \dfrac{\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}}{\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}}\)

\(\displaystyle t'(x) = \lim_{h\to0} \frac{\left(\sqrt{-3(x+h)-7}\right)^2 - \left(\sqrt{-3x-7}\right)^2}{h \left(\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}\right)}\)

\(\displaystyle t'(x) = \lim_{h\to0} \frac{(-3(x+h)-7) - (-3x-7)}{h \left(\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}\right)}\)

\(\displaystyle t'(x) = \lim_{h\to0} \frac{-3h}{h \left(\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}\right)}\)

\(\displaystyle t'(x) = -3 \lim_{h\to0} \frac1{\sqrt{-3(x+h)-7} + \sqrt{-3x - 7}}\)

The remaining limand is continuous at h = 0, so we can substitute h = 0 directly and get a limit/derivative of

\(\displaystyle t'(x) = -\frac3{\sqrt{-3(x+0)-7} + \sqrt{-3x - 7}} = \boxed{-\frac3{2\sqrt{-3x-7}}}\)

Answer:

182

Step-by-step explanation:

152

+31

---------

182

λ²e^(-λn) × 1 / y² is the joint probability density function of x1 and x2.

If x1 and x2 are two independent random variables,

The joint probability density function is equal to the product of the marginal distribution functions of two random variables if they are independent.

The joint probability density function of x1 and x2 is,

\(f(x1,x2) =\) λ² e^(-λ(x1 + x2))

consider

\(y1 = x1 + x2 ; \\y2 = e^{x1}\)

The joint probability density function of y1 and y2 is,

\(f(y1,y2) = f(x1,x2) . |J(x1,x2) |^{-1}\)

The Jacobean transformation on solving determinant is J(x1,x2)

\(J(x1,x2) =\) 1(0) - 1(eˣ¹)

= - (eˣ¹)

Now substituting values of y1 and y2

f(y1, y2) = λ² e^(-λ(x1 + x2)) . (\({\frac{1}{e^{x1} } }\))

since  

\(y1 = x1 + x2 ; \\y2 = e^{x1}\)

= λ²e^(-λn) × 1 / y²

Hence  λ²e^(-λn) × 1 / y² is the joint probability density function of y1 and y2.

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The value 2,649 represents the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 and the estimated population was 618.4.

The formula for population growth can be represented as:

P = P0ert

Here, P is the population of elephants, P0 is the initial population, e is the base of the natural logarithm, r is the rate of growth or decay, and t is the time in years.

Now, as per the given data, P = 2,649P0 = initial population r = 1.045 (as per the given expression)b = t - 1995 (as per the given formula)Now, putting these values in the population growth formula,

P = P0ert2,649 = P0e1.045(b-1995)Dividing by P0 on both sides, we get:e1.045(b-1995) = 2649/P0

Taking the natural logarithm on both sides,

ln e1.045(b-1995) = ln (2649/P0)

Applying the property of logarithm,1.045(b-1995) ln e = ln (2649/P0)1.045(b-1995) = ln (2649/P0)

vAs we need to find the value of P0, substitute the value of b = 0,1.045(0-1995) = ln (2649/P0)-1.045*1995 = ln (2649/P0)ln (2649/P0) = -2069.95

Taking anti-logarithm or exponentiation on both sides,2649/P0 = eln (2649/P0) = e^(-2069.95)2649/P0 = 4.29P0 = 2649/4.29P0 = 618.4

Therefore, the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 was 618.4.


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The critical heat flux (CHF) is the maximum heat flux that can be transferred from a surface to a boiling liquid before the boiling process transitions from a stable regime to an unstable regime. The CHF is an important parameter in the design of heat transfer systems, as exceeding the CHF can lead to boiling crisis, which can cause severe damage to the system.

The CHF for a fluid depends on various factors such as fluid properties, surface properties, and flow conditions. One of the commonly used correlations for calculating CHF is the Kutateladze number (Ku) correlation, which is given by:

q_c = C (ρ_L^2 g Δh_f)^0.5 (σ/ρ_L)^0.1

where q_c is the critical heat flux, ρ_L is the liquid density, g is the acceleration due to gravity, Δh_f is the latent heat of vaporization, σ is the surface tension, and C is a constant that depends on the surface properties and flow conditions.

Using this correlation, we can calculate the CHF for the given fluids at 1 atm:

For mercury at 1 atm:

Density of mercury, ρ_L = 13,534 kg/m^3

Latent heat of vaporization of mercury, Δh_f = 2.66 x 10^5 J/kg

Surface tension of mercury, σ = 0.48 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.028, we get:

q_c = 0.028 * (13,534^2 * 9.81 * 2.66 x 10^5)^0.5 * (0.48/13,534)^0.1

q_c = 2.44 x 10^6 W/m^2

For ethanol at 1 atm:

Density of ethanol, ρ_L = 789 kg/m^3

Latent heat of vaporization of ethanol, Δh_f = 8.51 x 10^5 J/kg

Surface tension of ethanol, σ = 0.022 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.027, we get:

q_c = 0.027 * (789^2 * 9.81 * 8.51 x 10^5)^0.5 * (0.022/789)^0.1

q_c = 1.17 x 10^6 W/m^2

For refrigerant R-134a at 1 atm:

Density of R-134a, ρ_L = 1245 kg/m^3

Latent heat of vaporization of R-134a, Δh_f = 2.03 x 10^5 J/kg

Surface tension of R-134a, σ = 0.011 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.026, we get:

q_c = 0.026 * (1245^2 * 9.81 * 2.03 x 10^5)^0.5 * (0.011/1245)^0.1

q_c = 1.35 x 10^6 W/m^2

For water at 1 atm:

Density of water, ρ_L = 1000 kg/m^3

Latent heat of vaporization of water, Δh_f = 2

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Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

The largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) is 15

Divisor of a Number :  

A Divisor is any number that divides a given number completely or with a reminder. Where a factor, is a divisor that divides the number entirely and leaves no remainder.

Here we have,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  

And n is a positive even integer  

For n = 2 ⇒  (2 + 1)(2 + 3)(2 + 5)(2 + 7)(2 + 9) = (3× 5 × 7 × 9 × 11 )    

For n = 4 ⇒   (4 + 1)(4 + 3)(4 + 5)(4 + 7)(4 + 9) = (5× 7 × 9 × 11 × 13 )

and so on.

From the above calculations,

we can say that (n + 1); (n + 3); (n + 5); (n + 7); (n + 9) are 5 consecutive odd numbers  

In every 5 consecutive odd positive integers,

One of them is always divisible by 3

And one of them is always divisible by 5.

Therefore,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5

As we know product of 3 and 5 = 15

then (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15

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The complete question is

What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?  

(A) 3         (B)  5        (C)  11          (D) 15             (E)  165    

The correct expression that represents the statement "Budweiser is bland if either Heineken is balanced or Foster's is refreshing" is option (c) B-(HVF).

Option (c) B-(HVF) represents the logical statement "Budweiser is bland (B) if not (-(HVF)) either Heineken is balanced (H), Foster's is refreshing (F), or both."

The statement states that Budweiser is bland if either Heineken is balanced or Foster's is refreshing. In logical terms, this can be represented as "Budweiser is bland if (Heineken is balanced) or (Foster's is refreshing)."

The expression B-(HVF) captures this logic. The '-' symbol denotes the negation or "not" operator. So, -(HVF) means "not (Heineken is balanced and Foster's is refreshing)."

The expression B-(HVF) states that Budweiser is bland if not both Heineken is balanced and Foster's is refreshing. This aligns with the given statement and correctly represents the logical relationship between Budweiser's blandness and the conditions related to Heineken and Foster's.

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The linear function that is parallel to y = 2x - 3 is given as follows:

y = 2x - 5.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

When two lines are parallel, they have the same slope, hence we need an equation with a slope of 2, given as follows:

y = 2x - 5.

The equation 1 is y = 2x - 3.

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